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Decomposition of a Rasch Partial Credit Item into Independent Binary and Indecomposable Trinary Items

Published online by Cambridge University Press:  01 January 2025

Huynh Huynh
Huynh Huynh*
Affiliation:
University of South Carolina
*
Requests for reprints should be sent to Huynh Huynh, Department of Educational Psychology, College of Education, University of South Carolina, Columbia, SC 29208.
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Abstract

For each Rasch (Masters) partial credit item, there exists a set of independent Rasch binary and indecomposable trinary items for which the sum of the scores and the partial credit score have identical probability density functions. If each indecomposable trinary item is further expressed as the sum of two binary items, then the binary items are positively dependent and cannot be both of the Rasch type.

Keywords

binary itemelementary symmetric functionsfree-response itemindecomposable itemgraded response modelpartial credit modelperformance assessmentopen-ended itemRasch modeltrinary item
Type
Original Paper
Information
Psychometrika , Volume 61 , Issue 1 , March 1996 , pp. 31 - 39
Copyright
© 1996 The Psychometric Society

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Footnotes

This paper was written while the author was working with Steve Ferrara and Hillary Michaels on some technical aspects of the Maryland School Performance Assessment Program. The author had been puzzled by the fact that most MSPAP assessment items have three or less score categories. With a psychometric justification now being apparent, this paper is dedicated to both of them.

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